Abstract
In this work, we combine our earlier proposed empirical potential based quasi-continuum theory, (EQT) [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys.127, 174701 (Year: 2007)10.1063/1.2793070], which is a coarse-grained multiscale framework to predict the static structure of confined fluids, with a phenomenological Langevin equation to simulate the dynamics of confined fluids in thermal equilibrium. An attractive feature of this approach is that all the input parameters to the Langevin equation (mean force profile of the confined fluid and the static friction coefficient) can be determined using the outputs of the EQT and the self-diffusivity data of the corresponding bulk fluid. The potential of mean force profile, which is a direct output from EQT is used to compute the mean force profile of the confined fluid. The density profile, which is also a direct output from EQT, along with the self-diffusivity data of the bulk fluid is used to determine the static friction coefficient of the confined fluid. We use this approach to compute the mean square displacement and survival probabilities of some important fluids such as carbon-dioxide, water, and Lennard-Jones argon confined inside slit pores. The predictions from the model are compared with those obtained using molecular dynamics simulations. This approach of combining EQT with a phenomenological Langevin equation provides a mathematically simple and computationally efficient means to study the impact of structural inhomogeneity on the self-diffusion dynamics of confined fluids.
This work was supported by the AFOSR, and NSF under Grant Nos. 0328162 (nano-CEMMS, UIUC), 0852657, and 0915718. T. Sanghi wishes to thank Sikandar Mashayak for confined water data, and Kumar Kunal and Ravi Bhadauria for helpful discussions. The authors acknowledge the use of the Taub cluster provided by the Computational Science and Engineering Program at the University of Illinois.
I. INTRODUCTION
II. PHENOMENOLOGICAL LANGEVIN EQUATION FOR CONFINED FLUIDS
A. Mean force profile
B. Random force modelR(t) and friction coefficient γ
III. SIMULATION DETAILS
IV. RESULTS
V. CONCLUSIONS
Key Topics
- Molecular dynamics
- 20.0
- Friction
- 19.0
- Langevin equation
- 13.0
- Rheology and fluid dynamics
- 13.0
- Self diffusion
- 12.0
Figures
COM density and PMF profiles of (a) carbon-dioxide, (b) water, confined inside a graphite slit. Δ is the empty region next to the pore wall. Solid line represents the results from EQT and open circle is MD result. The MD simulations details and the computation of the density and PMF profiles from the simulation trajectories are discussed in Refs. ^{ 10 } and ^{ 11 } .
COM density and PMF profiles of (a) carbon-dioxide, (b) water, confined inside a graphite slit. Δ is the empty region next to the pore wall. Solid line represents the results from EQT and open circle is MD result. The MD simulations details and the computation of the density and PMF profiles from the simulation trajectories are discussed in Refs. ^{ 10 } and ^{ 11 } .
Spatial variation of thermal noise for (a) carbon-dioxide, (b) LJ argon, confined inside a graphite slit. Thermal-ACFs are normalized by their initial values.
Spatial variation of thermal noise for (a) carbon-dioxide, (b) LJ argon, confined inside a graphite slit. Thermal-ACFs are normalized by their initial values.
Average temperature profile of the tracer particle during a Langevin simulation.
Average temperature profile of the tracer particle during a Langevin simulation.
(a) COM density Profile, ρ(z), (b) PMF Profile, W(z), (c) mean square displacement, MSD (inset: enlargement of MSD in 0–5 ps), (d) survival probability (inset: enlargement in 0–5 ps) of carbon-dioxide confined inside a H = 2.232 nm wide graphite slit. The average density, ρ_{ avg }, is 9.0 molecules/nm^{3} and temperature is 323 K. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result.
(a) COM density Profile, ρ(z), (b) PMF Profile, W(z), (c) mean square displacement, MSD (inset: enlargement of MSD in 0–5 ps), (d) survival probability (inset: enlargement in 0–5 ps) of carbon-dioxide confined inside a H = 2.232 nm wide graphite slit. The average density, ρ_{ avg }, is 9.0 molecules/nm^{3} and temperature is 323 K. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result.
(a)–(h) Comparison of MSD and survival probability of carbon-dioxide confined inside H = 1.860 nm (ρ_{ avg } = 8.7 molecules/nm^{3}, T = 348 K) and H = 1.488 nm (ρ_{ avg } =10 molecules/nm^{3}, T = 323 K) wide graphite slits. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result. (a, e) COM density; (b, f) PMF; (c, g) MSD; and (d, h) Survival probability.
(a)–(h) Comparison of MSD and survival probability of carbon-dioxide confined inside H = 1.860 nm (ρ_{ avg } = 8.7 molecules/nm^{3}, T = 348 K) and H = 1.488 nm (ρ_{ avg } =10 molecules/nm^{3}, T = 323 K) wide graphite slits. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result. (a, e) COM density; (b, f) PMF; (c, g) MSD; and (d, h) Survival probability.
(a)–(d) Comparison of MSD and survival probability of SPC/E water confined inside a H = 1.902 nm wide graphite slit with ρ_{ avg } = 30 molecules/nm^{3} and T = 300 K. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result. (a) COM density; (b) PMF; (c) MSD; and (d) Survival probability.
(a)–(d) Comparison of MSD and survival probability of SPC/E water confined inside a H = 1.902 nm wide graphite slit with ρ_{ avg } = 30 molecules/nm^{3} and T = 300 K. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result. (a) COM density; (b) PMF; (c) MSD; and (d) Survival probability.
(a)–(d) Comparison of MSD and survival probability of LJ argon confined inside a H = 1.690 nm wide graphite slit with ρ_{ avg } = 18.5 molecules/nm^{3} and T = 300 K. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result. (a) Density; (b) PMF; (c) MSD; and (d) Survival probability.
(a)–(d) Comparison of MSD and survival probability of LJ argon confined inside a H = 1.690 nm wide graphite slit with ρ_{ avg } = 18.5 molecules/nm^{3} and T = 300 K. Solid line represents the result from the combined Langevin-EQT (LE) model and dashed line is MD result. (a) Density; (b) PMF; (c) MSD; and (d) Survival probability.
Tables
Computation of the friction coefficient γ for confined systems.
Computation of the friction coefficient γ for confined systems.
Mean exit time and self-diffusion coefficient in different regions ^{ a } for confined CO_{2}.
Mean exit time and self-diffusion coefficient in different regions ^{ a } for confined CO_{2}.
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